Unveiling Time in Dose-Response Models to Infer Host Susceptibility to Pathogens

The biological effects of interventions to control infectious diseases typically depend on the intensity of pathogen challenge. As much as the levels of natural pathogen circulation vary over time and geographical location, the development of invariant efficacy measures is of major importance, even if only indirectly inferrable. Here a method is introduced to assess host susceptibility to pathogens, and applied to a detailed dataset generated by challenging groups of insect hosts (Drosophila melanogaster) with a range of pathogen (Drosophila C Virus) doses and recording survival over time. The experiment was replicated for flies carrying the Wolbachia symbiont, which is known to reduce host susceptibility to viral infections. The entire dataset is fitted by a novel quantitative framework that significantly extends classical methods for microbial risk assessment and provides accurate distributions of symbiont-induced protection. More generally, our data-driven modeling procedure provides novel insights for study design and analyses to assess interventions.

[1]  P. Young,et al.  Wolbachia-Mediated Resistance to Dengue Virus Infection and Death at the Cellular Level , 2010, PloS one.

[2]  Josep M. Pujol,et al.  The Effect of Ongoing Exposure Dynamics in Dose Response Relationships , 2009, PLoS Comput. Biol..

[3]  Tjalling Jager,et al.  Understanding toxicity as processes in time. , 2010, The Science of the total environment.

[4]  Karyn N. Johnson,et al.  Wolbachia and Virus Protection in Insects , 2008, Science.

[5]  R. Gray.  Modeling Survival Data: Extending the Cox Model , 2002 .

[6]  P. Grambsch,et al.  Modeling Survival Data: Extending the Cox Model , 2000 .

[7]  D. Ebert,et al.  A quantitative test of the relationship between parasite dose and infection probability across different host–parasite combinations , 2008, Proceedings of the Royal Society B: Biological Sciences.

[8]  J. Rose,et al.  Quantitative Microbial Risk Assessment , 1999 .

[9]  Karyn N. Johnson,et al.  Antiviral Protection and the Importance of Wolbachia Density and Tissue Tropism in Drosophila simulans , 2012, Applied and Environmental Microbiology.

[10]  Roman Ashauer,et al.  General unified threshold model of survival--a toxicokinetic-toxicodynamic framework for ecotoxicology. , 2011, Environmental science & technology.

[11]  Z. Xi,et al.  Wolbachia Induces Density-Dependent Inhibition to Dengue Virus in Mosquito Cells , 2012, PLoS neglected tropical diseases.

[12]  H. A. Druett.  Bacterial Invasion , 1952, Nature.

[13]  F. Jiggins,et al.  Wolbachia Variants Induce Differential Protection to Viruses in Drosophila melanogaster: A Phenotypic and Phylogenomic Analysis , 2013, PLoS genetics.

[14]  M. Elizabeth Halloran,et al.  A Frailty Mixture Model for Estimating Vaccine Efficacy , 1996 .

[15]  M. Ashburner,et al.  The Bacterial Symbiont Wolbachia Induces Resistance to RNA Viral Infections in Drosophila melanogaster , 2008, PLoS biology.

[16]  E. Miyaji,et al.  Controlled human infection and rechallenge with Streptococcus pneumoniae reveals the protective efficacy of carriage in healthy adults. , 2013, American journal of respiratory and critical care medicine.

[17]  Wopke van der Werf,et al.  Heterogeneous Host Susceptibility Enhances Prevalence of Mixed-Genotype Micro-Parasite Infections , 2011, PLoS Comput. Biol..

[18]  W A Furumoto,et al.  A mathematical model for the infectivity-dilution curve of tobacco mosaic virus: experimental tests. , 1967, Virology.

[19]  A. Beale,et al.  A study of polio vaccination in infancy: excretion following challenge with live virus by children given killed or living poliovaccine , 1966, Journal of Hygiene.

[20]  Karyn N. Johnson,et al.  Variation in Antiviral Protection Mediated by Different Wolbachia Strains in Drosophila simulans , 2009, PLoS pathogens.

[21]  M. Lipsitch,et al.  A Missing Dimension in Measures of Vaccination Impacts , 2014, PLoS pathogens.

[22]  Charles N Haas,et al.  Time‐Dose‐Response Models for Microbial Risk Assessment , 2009, Risk analysis : an official publication of the Society for Risk Analysis.

[23]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[24]  P. Hougaard.  A class of multivanate failure time distributions , 1986 .

[25]  T E Woodward,et al.  The Broad Street pump revisited: response of volunteers to ingested cholera vibrios. , 1971, Bulletin of the New York Academy of Medicine.

[26]  W A Furumoto,et al.  A mathematical model for the infectivity-dilution curve of tobacco mosaic virus: theoretical considerations. , 1967, Virology.

[27]  O. Aalen,et al.  Heterogeneity in survival analysis. , 1988, Statistics in medicine.

[28]  Thomas Walker,et al.  Wolbachia and the biological control of mosquito‐borne disease , 2011, EMBO reports.

[29]  E. Ionides,et al.  A dynamic dose–response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax , 2011, Journal of The Royal Society Interface.

[30]  F. O. Holmes.  Local Lesions in Tobacco Mosaic , 1929, Botanical Gazette.

[31]  A. Kleczkowski.  Interpreting relationships between the concentrations of plant viruses and numbers of local lesions. , 1950, Journal of general microbiology.

[32]  Heterogeneity in symbiotic effects facilitates Wolbachia establishment in insect populations , 2014, Theoretical Ecology.

[33]  David Huard,et al.  PyMC: Bayesian Stochastic Modelling in Python. , 2010, Journal of statistical software.

[34]  A H Havelaar,et al.  The Beta Poisson Dose‐Response Model Is Not a Single‐Hit Model , 2000, Risk analysis : an official publication of the Society for Risk Analysis.

[35]  M. Ashburner,et al.  The DrosDel Collection , 2004, Genetics.

[36]  Adi V. Gundlapalli,et al.  Quantitative Models of the Dose-Response and Time Course of Inhalational Anthrax in Humans , 2013, PLoS pathogens.

[37]  M E Halloran,et al.  Estimability and interpretation of vaccine efficacy using frailty mixing models. , 1996, American journal of epidemiology.